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Optics Letters

Broadband parametric processes in χ^(2) nonlinear photonic crystals

Matteo Conforti, Fabio Baronio, Martin Levenius, Katia Gallo

Published Jun 4, 2014• 13 citations
Publisher

Abstract

We develop a general model, based on a (2+1)D unidirectional pulse propagation equation, for describing broadband noncollinear parametric interactions in 2D quadratic lattices. We apply it to the analysis of twin-beam optical parametric generation in hexagonally poled LiTaO3, gaining further insights into experimental observations.
DOI
10.1364/ol.39.003457

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We review recent experimental and theoretical progress in the study of optical parametric generation and cascaded frequency up conversion in two-dimensional purely nonlinear lattices, relying on acoherent coupling of multiple resonances in the quadratic lattice. Since their original proposal (1), two dimensional (2D) nonlinear photonic crystals in periodically poled materials have been the subject of a number of experimental and theoretical investigations, exploring the enhanced possibilities to engineer the nonlinear dynamics of quadratic interactions afiorded in such structures (2,3). Most of the studies have concerned frequency up-conversion, until the recent demonstration of twin-beam optical parametric generation (TB-OPG) in 2D hexagonally poled crystals (4,5). TB-OPG experiments in hexagonally poled MgO:LiTaO3 lattices demonstrated enhanced para- metric gains as well as a rich spectral and angular response underpinned bythe coherent coupling of concurrent nonlinear processes throughshared signal or idlermodes. They provided evidence forrich interaction scenarios, generating multiple outputs in the infrared as well in the visible and encompassing also self-phase modulation and cascaded upconversion processes arising from the interplay of multiple lattice resonances.A good agreement was found with a simple model in- volving the cross-seeding of two non-collinear OPG processes via a common signal (idler), while the development of advanced ad-hoc simulation tools enabled to fully account for the complex nonlinear dynamics in the 2D lattices and faithfully reproduce the rich spectral-angular response seen in the experiments (6).
Summary form only given. The efficiency and engineering capabilities afforded by parametric processes in second-order [χ(2)] nonlinear media have tremendously benefitted from periodic poling technologies in ferroelectric materials such as LiNbO3, nowadays routinely exploited in optical parametric generators, amplifiers and oscillators, as well as high brightness sources of entangled photons [1, 2]. Nonlinear photonic crystals (NPCs) implemented by periodic poling, have also attracted a great deal of attention, since they provide additional degrees of freedom to coherently shape the angular and spectral response of parametric devices [3-4]. Following the first demonstration of coherently coupled twin-beam optical parametric generation (OPG) in a χ(2)NPC [4], a number of studies investigated their potential for classical and quantum applications [5-6].Here we demonstrate twin beam OPG in a hexagonally poled LiTaO3 NPC pumped at 527 nm and generating signal and idlers in the near-infrared (λS~800 nm) and telecom (λI~1550nm) ranges. We perform a complete spectral and angular mapping of its OPG response for different pump pulse energies (10 - 100μJ) and incidence angles (-2.5 to 2.5°), finding very good agreement between predictions (Fig. 1b-c) and experiments
In this work the properties of light produced by spontaneous parametric downconversion (SPDC) in 2D nonlinear lattices have been studied. A quantum mechanical model of 2D SPDC was formulated, solved in the general case, and analyzed in the special case when two di erent signals are coupled as a consequence of their idlers being degenerate in frequency and spatial propagation. According to the model these 'twin signals' are correlated in phase and amplitude, and the gain coe cient of the coupled processes enhanced by a factor √ 2. The analytically derived correlations and the gain enhancement was supported experimentally by measurements on a hexagonal lattice in a LiTaO3 crystal.
We study parametric interactions in a new type of nonlinear photonic structure, which is realized in the volume between a pair of nonlinear crystals. In this kind of structure, which we call binary, multiple nonlinear optical processes can be implemented simultaneously, owing to multiple phase-matching conditions, fulfilled separately in the constituent crystals. The coupling between the nonlinear processes by means of modes sharing similar frequency is attained by the spatially broadband nature of the parametric fields. We investigate the spatial properties of the fields generated in the binary structure constructed from periodically poled crystals for the two examples: (1) single parametric downconversion and (2) coupled parametric downconversion and upconversion processes. The efficacy of the fields’ generation in these examples is analyzed through comparison with the cases of a traditional single periodically poled crystal and an aperiodic photonic structure, respectively. For this, we have devised a method that allowed us to solve the field equations numerically without resorting to statistically modeling the input vacuum states. It has been shown that the relative shift between the periodic crystal lattices has a crucial effect on the generated spatial field spectrum and overall efficiency. In addition, the influence of the intercrystal distance on these characteristics has been studied. Therefore, our study suggests that one can construct optical elements with sophisticated nonlinear properties from simpler elements without significant sacrifice of efficacy.